Divisors,measures and critical functions

In [4] we have introduced a new distance between Galois orbits over ℚ. Using generalized divisors, we have extended the notion of trace of an algebraic number to other transcendental quantities. In this article we continue the work started in [4]. We define the critical function for a class of transcendental numbers, that generalizes the notion of minimal polynomial of an algebraic number. Our results extend the results obtained by Popescu et al [5].     

Diffusion coefficient and shear viscosity of rigid water models

We report the diffusion coefficient and viscosity of popular rigid water models: two non-polarizable ones (SPC/E with three sites, and TIP4P/2005 with four sites) and a polarizable one (Dang-Chang, four sites). We exploit the dependence of the diffusion coefficient on the system size (Yeh and Hummer 2004 J. Phys. Chem. B 108 15873) to obtain the size-independent value. This also provides an estimate of the viscosity of all water models, which we compare to the Green-Kubo result. In all cases, a good agreement is found. The TIP4P/2005 model is in better agreement with the experimental data for both diffusion and viscosity. The SPC/E and Dang-Chang models overestimate the diffusion coefficient and underestimate the viscosity.     

Bifibrations and Weak Factorisation Systems

We review a theorem of A. Roig about Quillen model structures on Grothendieck bifibrations and observe that it contains a gap. We reformulate one of its assumptions in order to validate it. As an application to the new version, we introduce the fibred model structure on the category of small categories enriched in a suitable monoidal model category.     

Carotid plaque high-resolution MRI at 3 T: evaluation of a new imaging score for symptomatic plaque assessment

Purpose

To assess the sensitivity and specificity of intra-plaque hemorrhage (IPH), large lipid-rich necrotic core (LR-NC) and ulceration or cap rupture (UCR) for symptomatic carotid plaque characterization and to evaluate a new imaging score [Hemorrhage, Ulceration or cap rupture, Lipid-rich necrotic Core (HULC) score based on the sum of presence/absence of IPH, UCR and LR-NC; range 0–3] for assessment of recently symptomatic carotid plaques.

Material and methods

Twenty-seven recently symptomatic (< 8 weeks) and 36 asymptomatic patients with a carotid plaque thicker than 2 mm were prospectively imaged on a 3-T magnetic resonance (MR) system using high-resolution, multi-contrast MR sequences. Prior to analysis, all images were reviewed to assess image quality of each sequence. Sensitivity and specificity of IPH, LR-NC, UCR and HULC scores were calculated.

Results

Fifty-one patients were analyzed (26 symptomatic carotids and 67 asymptomatic carotids) after exclusion of studies with poor image quality. Sensitivity and specificity for symptomatic carotid plaque was, respectively, 46.1% and 97% for IPH, 84.6% and 73.1% for UCR and 80.7% and 76.1% for LR-NC. A HULC score of 2 or more showed a sensitivity of 73% and a specificity of 92.5%.

Conclusion

At 3 T, intra-plaque hemorrhage is the most specific criterion to characterize symptomatic carotid plaque. The HULC score offers the best compromise between sensitivity and specificity.     

Dual action of Impurities in Crystal Growth from Solutions

A dual action of impurities becomes evidently in growth kinetic of prismatic faces of KDP. At higher supersaturation two-dimensional nucleation mechanism due to impurities prevails. At smaller supersaturation the blocking effect of the steps created by the dislocation mechanism of growth become efficient. The limit of the “dead” growth zone depending on the impurity's concentration and the solution pH is a result of this last effect and agrees with the Cabrera-Vermilyea mechanism.